Group structure in finite coverings of compact solenoidal groups (Q5925784)

It is shown that for any \(n\)-fold covering \(p:X\to G\) of a compact solenoidal group \(G\) by a connected topological space \(X\) the space \(X\) admits a compatible topological group structure turning \(p\) into a homomorphism between compact Abelian groups. A topological group \(G\) is solenoidal provided it admits a continuous group homomorphism \(h:\mathbb R\to G\) from the additive group of real numbers whose image \(h(\mathbb R)\) is dense in \(G\).